Galois Relations on Knot InvariantsWe discuss the existence of Galois relations obeyed by certain link invariants. Some of these relations have recently been identified and exploited within the context of CFT and Lie/Kac-Moody…T. Gannon, M. A. Walton·Sep 17, 1995SaveLearn
L Operators and Quantum Enveloping AlgebrasThe relations between L operators and the generators in the quantum enveloping algebras are studied. The L operators for UqAN and UqG2 algebras are explicitly…Mi Xie, Bai-Qi Jin, Zhong-Qi Ma·Sep 14, 1995SaveLearn
Atypical Representations of Uq(sl(N)) at Roots of UnityWe show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of Uq(sl(N)) when q is root of unity. The explicit construction of atypical…Boucif Abdesselam·Sep 13, 1995SaveLearn
Quantum Homogeneous Spaces as Quantum Quotient SpacesWe show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of…Tomasz Brzezinski·Sep 13, 1995SaveLearn
Quantum Deformations of the Self-Duality Equation and Conformal TwistorsA noncommutative algebra of the complex q-twistors and their differentials is considered on the basis of the quantum GLq (4)× SLq (2) group. Real and pseudoreal q-twistors are discussed…B. M. Zupnik·Sep 12, 1995SaveLearn
The Modified q-Bessel Functions and the q-Bessel-Macdonald FunctionsWe define a q-analog of the modified Bessel and Bessel-Macdonald functions. As for the q-Bessel functions of Jackson there is a couple of functions of the both kind. They are arisen in the Harmonic…M. A. Olshanetsky, V. -B. K. Rogov·Sep 11, 1995SaveLearn
On the Fundumental Invariant of the Hecke Algebra Hn(q)The fundumental invariant of the Hecke algebra Hn(q) is the q-deformed class-sum of transpositions of the symmetric group Sn. Irreducible representations of Hn(q), for generic q,…J. Katriel, B. Abdesselam, A. Chakrabarti·Sep 11, 1995SaveLearn
Non--Minimal q--Deformations and Orthogonal Symmetries: Uq(SO(5)) ExampleNon--minimal q-deformations are defined. Their role in the explicit construction of the matrix elements of the generators of Uq(SO(5)) on suitably parametrized bases are exhibited. The…B. Abdesselam, D. Arnaudon, A. Chakrabarti·Sep 11, 1995SaveLearn
On Ohtsuki's invariants of integral homology 3-spheres, IAn attempt is made to conceptualize the derivation as well as to facilitate the computation of Ohtsuki's rational invariants λn of integral homology 3-spheres extracted from Reshetikhin-Turaev…Xiao-Song Lin, Zhenghan Wang·Sep 8, 1995SaveLearn
A q-Lorentz Algebra From q-Deformed Harmonic OscillatorsA mapping between the operators of the bosonic oscillator and the Lorentz rotation and boost generators is presented. The analog of this map in the q-deformed regime is then applied to q-deformed…A. Ritz, G. C. Joshi·Sep 8, 1995SaveLearn
The HOMFLY polynomial for links in rational homology 3-spheresWe construct a polynomial invariant, for links in a Seifert fibered or atoroidal rational homology 3-sphere, which generalizes the 2-variable Jones polynomial (HOMFLY). As a consequence, we show that…Efstratia Kalfagianni, Xiao-Song Lin·Sep 8, 1995SaveLearn
A Coassociative C*-Quantum Group with Non-Integral DimensionsBy weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C*-Hopf algebra, which is…G. Bohm, K. Szlachanyi·Sep 8, 1995SaveLearn
Two-Rowed Hecke Algebra Representations at Roots of UnityIn this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra Hn(q) of type An-1 in the non-generic case where q is a root of unity.…T. A. Welsh·Sep 7, 1995SaveLearn
Twisted representations of vertex operator algebrasLet V be a vertex operator algebra and g an automorphism of finite order. We construct an associative algebra Ag(V) and a pair of functors between the category of Ag(V)-modules and a…Chongying Dong, Haisheng Li, Geoffrey Mason·Sep 6, 1995SaveLearn
Noncommutative Geometry of Finite GroupsA finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding…K. Bresser, A. Dimakis, F. Mueller-Hoissen et al.·Sep 6, 1995SaveLearn
Exact operator solution of the Calogero-Sutherland modelThe wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with…Luc Lapointe, Luc Vinet·Sep 5, 1995SaveLearn
A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjectureA formula of Rodrigues-type for the Jack polynomials is presented. It is seen to imply a weak form of a conjecture of Macdonald and Stanley.Luc Lapointe, Luc Vinet·Sep 5, 1995SaveLearn
On the Drinfel'd-Kohno Equivalence of Groups and Quantum GroupsA method to calculate matrix representations of the twist element of Drinfel'd -- chosen to be unitary -- is given and illustrated at some examples. It is observed that for these F-matrices…Ralf A. Engeldinger·Sep 5, 1995SaveLearn
(T*B)q, q-analogue of model space and CGC generating matricesWe study relations between the deformed cotangent bundle (T*B)q for the Borel subgroup B of a given simple Lie group G, the quantum Lie algebra Jq associated with the corresponding quantum group…A. G. Bytsko, L. D. Faddeev·Aug 29, 1995SaveLearn
The bicovariant differential calculus on the kappa-Poincare group and on the kappa-Minkowski spaceThe bicovariant differential calculus on the four-dimensional kappa-Poincare group and the corresponding Lie-algebra like structure are described. The deifferential calculus on the n-dimensional…P. Kosinski, P. Maslanka, J. Sobczyk·Aug 28, 1995SaveLearn
Remarks on central extensions of the Galilei group in 2+1 dimensionsSome properties of central extensions of 2+1 dimensional Galilei group are discussed. It is shown that certain families of extensions are isomorphic. An interpretation of new nontrivial cocycle is…Y. Brihaye, S. Giller, C. Gonera et al.·Aug 28, 1995SaveLearn
On inner product in modular tensor categories. IIn this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups…Alexander Kirillov·Aug 24, 1995SaveLearn
Real Forms of the Oscillator Quantum Algebra and its RepresentationsWe consider the conditions under which the q-oscillator algebra becomes a Hopf *-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore,…C H Oh, K Singh·Aug 24, 1995SaveLearn
Affine Hecke algebras associated to Kac-Moody groupsIn this paper we give a geometric construction of Cherednik's double affine Hecke algebra. We construct the algebra as the equivariant K-theory of the Lagrangian subvariety of the cotangent…H. Garland, I. Grojnowski·Aug 24, 1995SaveLearn
Regularity of rational vertex operator algebrasA regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient…Chongying Dong, Haisheng Li, Geoffrey Mason·Aug 24, 1995SaveLearn